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My understanding is that it's like two of the same scratch-off lottery ticket. There are two spots you can scratch, only one has a prize, we don't know which one that is but it's same for both tickets. The tickets are taken to separate rooms. The people in each room then pick a spot and scratch it. How likely is it that at least one of them will win?

The odds of one scratch winning are of course 50%, and the odds of the other person winning are of course also 50%. The odds of both people winning are 25%, and both people losing also 25%.

The CHSH experiment suggests otherwise: that when one person loses the other person is less likely to also lose, such that the likelihood of both losing is only 15%. How can this happen? I haven't a clue. I'm not a theoretical physicist, and I haven't personally conducted this (~ $5,000) experiment. But it's a result that deeply bothers me.

If you build this system you can then scratch a whole lot of tickets. Each ticket has a 50% chance of a side having the prize, but as long as both parties are consistently scratching the same side of entangled pairs they will win more often than they lose, revealing whether or not they are in agreement. I have no idea how this could be true, but people keep running the experiment and keep getting similar results. And, it seems like this could result in faster than light communication, so there's probably a better ELI-5 out there.

> The CHSH experiment suggests otherwise: that when one person loses the other person is less likely to also lose, such that the likelihood of both losing is only 15%. How can this happen? I haven't a clue.

That’s easy, even without quantum mechanics. All you need is to have a different distribution of lottery tickets. Print tickets such that, if one wins, the other is more likely to win, which you can do by having the number of winning spots per ticket be random and correlated. For example, there could be a 50% chance that neither ticket has a winning spot and a 50% chance that each ticket has one winning spot.

But you could imagine a pair of tickets with internal radios, such that, when you scratch one, it tells the other one, and together they simulate a general function where the joint probability of (win on ticket 1, win on ticket 2). If you set up the probabilities appropriately, then you can’t use the tickets to send a signal, and the result is referred to in the literature as “non-signaling boxes” (the magic tickets are the boxes).

Quantum mechanical entanglement can do something like this, except that the probability distributions you can generate with entanglement are a subset of the more general non-signaling boxes.

> Print tickets such that, if one wins, the other is more likely to win, which you can do by having the number of winning spots per ticket be random and correlated.

In order to refute this you need to get into the CHSH experiment's design, which doesn't use the raw detection rate but compares detections that should not have similar results. Imagine that both tickets have a prize on the right side, and both participants have agreed to always choose the left side. CHSH predicts that some of the time the prize will change sides: but, crucially, only from the losing side to the winning side, and only if the other ticket lost, and even if the tickets are revealed close enough in time that a signal could not propagate between them.

The conclusion of CHSH is that detections are correlated to the angle between the sensors, and not the angle between the sensors and the source.

This makes absolutely no sense. There is no such thing as a winning or losing side until it's been scratched, and even if the ticket were able to randomly switch from a loser to a winner, how would it ever know that the other ticket was also a loser? And if it's true that detection is correlated to the angle between detectors, it seems easy enough to build a statistical system around variable sensor angles that is able to communicate instantaneously.

I might not have interpreted everything you said, either. Internet forums aren't the best way to discuss deep problems.

> In order to refute this

Refute what? I'm pointing out that classical (non-quantum) scratch-off lottery tickets can have the property you described. This is only thematically related to the CHSH game, and I'm rather confused as to what you're trying to say.

The Wikipedia articles about the CHSH inequality are IMO quite bad. The conclusion of CHSH has approximately nothing to do with measurement angles. Here's what CHSH is saying, based on one formulation, which is IMO far, far nicer than Wikipedia's and makes the same point.

1. There's a game that two players could play (with the help of a neutral third party). The neutral third party picks random bits x and y, tells player A the value of x and tells player b the value of y. Each player then chooses a play (A's play is a and B's is b) according to whatever strategy they like, except that they can't communicate. They are allowed to communicate with each other beforehand, though. You can look at sites like this for more details about the game works: https://circles.math.ucla.edu/circles/lib/data/Handout-2987-...

2. If A and B are only allowed to choose random numbers (jointly before the game and separately once it starts) and do local calculation, then they cannot win with more than a certain probability. This is the CHSH inequality, and it's a statement about classical statistics.

3. If A and B are allowed to produce an entangled state before the game and each hold on to one part of the state, then they can make measurements on their parts once the game starts and use those measurements as part of a better strategy. This strategy wins with probability higher than the CHSH inequality allows.

> I'm pointing out that classical (non-quantum) scratch-off lottery tickets can have the property you described.

No, if A always scratches the left, and B alternates between left and right, your classical trick of having some tickets with two winners and some with two losers won’t produce the correct win distributions for B’s choices.

The CHSH game is an attempt at explaining the experiment. The core of CHSH is a formula describing an expected distribution: `S = E(a, b) - E(a, b') + E(a', b) + E (a', b')`, where classical explanations can achieve an S with magnitude approaching 2. Experiments arriving at an S > 2 are said to support the quantum theory.

> No, if A always scratches the left, and B alternates between left and right, your classical trick of having some tickets with two winners and some with two losers won’t produce the correct win distributions for B’s choices.

My proposal was intended to be independent of A and B’s strategy. As a fully worked-out example, suppose the tickets are printed like this:

With probability 42.5%: all positions win

With probability 42.5%: all positions lose

With probability 7.5%: Both of A’s options win and both of B’s options lose

With probability 7.5%: Both of A’s options lose and both of B’s options win.

This follows the rules of the game, and it has the following properties. A wins with probability 50% regardless of their strategy, as does B. And A and B get the same outcome 85% of the time.

For the CHSH inequality (following the pretty-bad Wikipedia article), each E term is the probability that A and B both win when they use the indicated strategies, which is 0.425. So S=0.85, which is well within the limit, as it should be since these are extremely boring classical tickets.

My point wasn't to derive the best classical strategy, but to describe the problem in simple terms that people who aren't familiar with quantum mechanics could understand. QM is a very academic field, verging on intentionally obtuse, and that keeps non-experts from participating. Cozy if you're entrenched, but not the best for fresh approaches.

> Many quantum information theorists don’t even believe the wave function is “real” but just a mathematical tool for making predictions about measurement outcomes

You are correct that many say this, but this is a constant source of frustration for me (a physicist who does believe the wave function is the only real thing). These physicists never seem to articulate what then is supposed to actually be “real” (under their definition) or what laws govern the “real” things as opposed to the wave function. Implicit seems to be that there is some kind of separate classical realm that obeys non quantum mechanical laws. Is this separate classical realm to be understood as a macroscopic limit of the quantum realm? But if so then the whole picture is circular since wavefunctions are supposed to be mere bookkeeping devices for classical things.

Or to put this more succinctly, if the wave function is a mere bookkeeping device, then bookkeeping for __what__?

(I should mention that yes I know about QBism and all that and my confusion is not for lack of talking to QBists about such things — I just can’t make heads or tails of what they tell me!)

> bookkeeping for __what__?

Bookiping for things that happen so fast and at such a small scale that our current technological tools cannot fully capture data with enough precision and accuracy for us to make an good model of the underlying behaviour.

Imagine you put a spinning ball on top of a frozen lake on a windy day. You are going to observe the ball spin continously towards the same orientation until several gusts of wind make it spin the other way around, and this goes on and on for hours. From the measurements of the wind and current spin of the ball, you can make a model that accurately and precisely predicts the spin of the ball on the almost frictionless frozen lake.

Now imagine your spinning ball is extremely small you can't even see it or any "wind" with any tools that you currently have, but you can still measure its spin to a certain precision. Now imagine this "wind" is so strong and volatile that the tools you have sometimes takes a somewhat accurate physical snapshot of it and sometimes it just misses the gust. You take a look at the somewhat accurate measured spin and it seems to have changed without any reason, but it was just because your tooling is not accurate and precise enough to capture all the quantum gusts of wind that influence the quantum ball, so it looks like the ball is changing its spin randomly, whist in reality, we just can't precisely measure whatever is influencing the ball's spin with our current tooling. The influences are there, it's just that our tooling can't capture them precisely and accurately enough.

To combat that, we continously measure the ball's spin and we are able to figure out a pattern, not a precise one (because again, our tooling is not precise and accurate enough), but a pattern based on probability of the ball being in a specific spin state, we can even combine this with our inaccurate measurements of the quantum wind and further improve the accuracy of the probability. But never to a precise pattern, because our tooling sometimes misses certain wind states that it looks like the ball chagend spin randomly.

If we had tools that precisely and accurately measured the ball's spin and the quantum wind, we would be able to build a precise and accurate model of the spin based on those measurements. But we can't, although, we still want to make science around these inaccurate measurements, and probability based patterns are just enough for the science we want to make.

The wave function is just the result of our lack of precise and accurate measuring tools and measuring methods at this quantum scale. And for now, it's good enough for the science we want to do.

You describe a local hidden variable theory such as has been definitively ruled out by Bell/CHSH inequality experiments (see, e.g. (2022 Nobel Prize)[https://www.nobelprize.org/all-nobel-prizes-2022/] ).

But even if you could make some baroque version of a model like this (with the position of one ball instantaneously reacting to other far away balls perhaps and some pilot waves) invoking it still wouldn’t answer my question about ontology. Implicit in this description seems to be the existence of a separate non-quantum realm (little balls that spin, jostled by “wind”). What are these balls supposed to be made of? If not atoms (since atoms are stable by virtue of quantum mechanics, which you seek to explain), then why don’t they suffer from ultraviolet catastrophes? Hopefully you see my point.

Maybe it's things smaller than whatever smallest thing we have been able to measure.

I'll read up the inequality experiment.

I would describe classical correlations as downgraded entanglement. Correlation is what's left when entanglement decoheres / undergoes uncontrolled phase noise. Things you should be able to do, like win the Mermin-Peres magic square game 100% of the time, aren't possible when the entangled qubits you'd use to do it aren't protected from phase noise.

Decoherence is sort of analogous to air. It's so ubiquitous in your life that you don't really think about it, but you'd notice immediately if it was removed. Being steeped in air your whole life has twisted your physical intuitions. That's why Aristotle thought "objects come to rest" when actually objects move at constant speed unless acted upon by a force. Similarly, being steeped in decoherence has twisted your physical intuitions. Like thinking "adding more ways for something to happen must make it more likely" or "a particle's position is independent of its momentum" or "I can measure an object without affecting it". But actually different paths can interfere, and momentum is the Fourier transform of position, and measurements apply phase noise.

Decoherence is so ubiquitous that it's a huge challenge to engineer systems that suppress it. This is why quantum computers are so hard to make, and why quantum error correction has so much more overhead compared to classical error correction. Classical error correction only has to fix bit flips, and it can do so by making phase flips worse (which it does). Quantum error correction has to simultaneously fix bit flips and phase flips.

When two particles are entangled, rotating one around the X axis by an angle A and the other by an angle B and then measuring produces measurement results that agree with probability cos^2(A-B). Same as the probability of a photon with polarization angle A passing through a polarizing filter with angle B. Decohere the entanglement before the rotations, and the measurements will instead agree with probability cos^2(A)cos^2(B) + sin^2(A)sin^2(B). Note that cos^2(A-B) = cos^2(A)cos^2(B) + sin^2(A) sin^2(B) + 2 cos(A) cos(B) sin(A) sin(B), meaning decoherence is taking away the 2 cos(A) cos(B) sin(A) sin(B) interference term. That's the downgrade. That's what makes your best possible CHSH win rate drops from 85% to 75%. If entanglement allowed sending messages, the initial CHSH win rate would be 100% instead of 85%.

Thanks. So how is it not analogous to the glove example?

It's a trick question. Gloves go in a glove box.

Yeah really, they didn't give any example of the "more"...

The gloves doesn't change their state when you check on them. Quantum particles do.

Example: Lets say you check if the glove is white or black, you see it is white. Then you check if the glove is half white/half black, or half black/half white, you see it is half white/half black. Then you check again if it is white or black, now it is black. That is how quantum gloves would work, but real gloves doesn't work that way.

>Then you check again

You only get to check once, I think. The rest doesn't matter, supposedly.

That is false, it changes every time you check along another axis. If you make the same check it doesn't change, but if you change what you check then you can update the particle as my example shows.

Changing a particle like this by making repeated measurements is a standard example in undergrad quantum mechanics.

Edit: There is always a part of the particles state that you can't know, you know Heisenberg's indeterminacy principle, so if you measure position you now makes velocity undetermined, and then if you measure velocity now you make position undetermined, and then if you go back and try to measure position the particle will be in a new random spot.

So if you check that the gloves are black they are black every time you check (axis 1). And then if you check that they have five fingers, they have five fingers every time(axis 2).

So, it sounds exactly like a "gloves in a box" example, right?

I'm not trying to be cheeky, I'm just pointing out that the example really does sound analogous, as stated so far.

It depends on how those states interact with each other. Lets say you can't know a gloves fingers and a gloves color at the same time, so checking number of fingers resets the color and checking color resets number of fingers.

Then if you check number of fingers many times, you get the same result every time. But if you alternate checking fingers and color, you will get random results every time.

Edit: Not that I'm saying this is what original poster meant, just that this is the main difference between quantum particles and our macroscopic objects like gloves.

Very good clarification.

In my mind, I see it like you've got a line bisecting another line. You don't know what the angles are until you measure one, and once you measure it, you know for certain what the other angle is, whether that person does or not. But you can't change the angle and you can't send information using them.

Except the line is spinning around faster than you can see and you measuring it makes it stop. Your example makes it sound like the angle was decided before you measured.

Feynman explains quantum correlation using boxes with 3 buttons https://youtube.com/watch?v=ZcpwnozMh2U&t=17m55s

"it does not matter who measures"